The long-term goal of this project is to develop statistical methods and software for the analysis of genetic basis of complex traits. In spite of the rapid progress in the development of high-resolution SNP maps of the human genome, the task of identification and characterization of susceptibility genes for complex diseases is one of the greatest challenges facing human geneticists. This challenge is partly due to the limitations of current statistical methods for detecting gene effects that depend solely or partially on interactions with other genes and with environmental exposures. For complex diseases, each individual gene has a very small effect and this small effect may be further confounded by population stratification for population-based studies. Therefore, it is difficult to detect the genetic effect when the gene is analyzed individually. This project will develop statistical methods that analyze a group of loci to identify a set of susceptibility loci, to detect high order gene-gene interactions and gene-environment interactions, and to understand the genetic architecture of complex diseases. These methods will accelerate the discovery of the genes responsible for complex diseases and hold great promise for the development of new diagnostics tools and treatments for human diseases. When searching for a set of susceptibility markers from hundreds of SNPs, an objective function that can consider high order gene-gene interaction will be introduced, and a dimension reduction technique will be needed. Finally, when searching for a set of susceptibility markers across the genome, the computational feasibility will be the main concern. An simulated annealing search method will be introduced to detect a set of markers whose interactions are responsible for the disease. At the same time, the computational burden will be kept within the ability of the current technology. The proposed methodology will be implemented by user-friendly software. The documentation, distribution, and support of the software will be provided.